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3D Ultrasound Imaging: Fast and Cost-effective Morphometry of Musculoskeletal Tissue
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A Second Order Multi-Stencil Fast Marching Method with a Non-Constant Local Cost Model.

Susana Merino-Caviedes, Lucilio Cordero-Grande, Maria Teresa Perez

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    This study introduces a modified Multi-Stencil Fast Marching Method (MSFM) for improved image processing accuracy. The enhanced scheme accounts for local cost variations and offers robustness through permutation-invariant stencils.

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    Area of Science:

    • Computational Mathematics
    • Image Processing
    • Numerical Analysis

    Background:

    • The Fast Marching Method (FMM) is a fundamental algorithm in image processing.
    • The Multi-Stencil Fast Marching Method (MSFM) was developed to enhance FMM accuracy.
    • Existing MSFM methods may not fully account for local cost variations.

    Purpose of the Study:

    • To propose a modified numerical scheme for MSFM that incorporates local cost variations.
    • To analyze the impact of stencil set selection on MSFM accuracy.
    • To evaluate the robustness of the proposed MSFM scheme.

    Main Methods:

    • A modified numerical scheme for MSFM is developed, achieving second-order accuracy.
    • The influence of stencil orthogonality and axis swapping is investigated.
    • Stencils are selected from neighborhoods of varying radii.
    • Permutation-invariant stencil sets are explored for robustness.

    Main Results:

    • The proposed MSFM schemes demonstrate improved accuracy compared to original methods.
    • The modified scheme effectively handles local cost variations.
    • Permutation-invariant stencil sets enhance robustness against shifted vector coordinates.

    Conclusions:

    • The modified MSFM offers superior accuracy and robustness in image processing applications.
    • Careful selection of stencil sets is crucial for MSFM performance.
    • The proposed method advances the state-of-the-art in numerical schemes for image analysis.